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Abstract

Using a large number of specially selected imaginary object colors which are metameric with respect to one set of color-mixture functions, the spatial distribution of these colors with respect to the other set of color-mixture functions provides an illustrative means of measuring the total difference of the two sets of color-mixture functions. The spatial distribution follows a normal trivariate distribution law which allows the computation of an ellipsoid that is expected to contain 95% of all theoretically and practically possible object colors of the same class used to calculate that ellipsoid. A numerical example involving the color-mixture functions of the 1931 CIE standard observer and the color-mixture functions derived from the Stiles 10° pilot data demonstrates the theory.

References

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Table I

Classification of the difference between two sets of color-mixture functions (c.m.f.).a

Type

1

ūi′ (λ) = Σjaijūj(λ)

ūi′ (λ) = Σj aijūj(λ)/Σj cjūj(λ) cj = Σi aij

2

ῡi(λ)=t(λ)ūi(λ)

υi(λ) = ūi(λ)

3

w¯i(λ)=σi(λ)ūi(λ)

wt(λ) = σi(λ)ūi(λ)/Σjσj(λ)ūi(λ)

aūi(λ) denotes the reference set of c.m.f.; ūi′ (λ),
ῡi(λ),
w¯i(λ) denote three types of c.m.f. which differ in three characteristic ways from the reference set ūi(λ). ui(λ), ui′ (λ), υi(λ), wi(λ) denote chromaticity coordinates of the spectrum colors with respect to their corresponding sets of c.m.f. The types of difference between two sets of c.m.f. is characterized by the conversion functions: aij, t(λ), σi(λ), respectively.